In many such cases, it is likely that the graft is rejected because the recipient is sensitized to proteins on donor cells, including bone marrow cells, by blood transfusions. The formation of memory immune cells is a hallmark of sensitization, and these memory cells are relatively insensitive to chemotherapy and radiation. Alefacept, a drug used to treat psoriasis, on the other hand, selectively depletes these cells. The investigators are conducting a pilot study to begin to determine whether incorporating alefacept into a low dose conditioning regimen can effectively mitigate sensitization and, thereby, prevent rejection of allogeneic blood and marrow transplants for multiply transfused children with non-malignant hematological diseases.